Natural width of the superconducting transition in epitaxial TiN films

We investigate the effect of various fluctuation mechanisms on the DC resistance in superconducting devices based on epitaxial titanium nitride (TiN) films. The samples we studied show a relatively steep resistive transition (RT), with a transition width $ΔT/T_\mathrm{c} \sim 0.002-0.025$, depending on the film thickness (20 nm, 9 nm, and 5 nm) and device dimensions. This value is significantly broader than expected due to conventional superconducting fluctuations ($ΔT/T_\mathrm{c} \ll 10^{-3}$). The shape and width of the RT can be perfectly described by the well-known effective medium theory, which allows us to understand the origin of the inhomogeneity in the superconducting properties of TiN films. We propose that this inhomogeneity can have both dynamic and static origins. The dynamic mechanism is associated with spontaneous fluctuations in electron temperature (T-fluctuations), while the static mechanism is due to a random spatial distribution of surface magnetic disorder (MD). Our analysis has revealed clear correlations between the transition width and material parameters as well as device size for both proposed mechanisms. While T-fluctuations may contribute significantly to the observed transition width, our findings suggest that the dominant contribution comes from the MD mechanism. Our results provide new insights into the microscopic origin of broadening of the superconducting transition and inhomogeneity in thin superconducting films.